Question

divide the polynomial2x⁴-2x²-2x-5by(x-1) and verify by using the remainder theroem​

Answer 1

Step-by-step explanation:

Let f(x)=2x4−4x3−3x−1

First see how many times 2x4 is of x.

x2x4=2x3

Now multiply (x−1)(2x3)=2x4−2x3

Then again see the first term of the remainder that is −2x3. Now do the same.

Here the quotient is 2x3−2x2−2x−5 and the remainder is −6.

Now, the zero of the polynomial (x−1) is 1.

Put x=1 in f(x),f(x)=2x4−4x3−3x−1

f(1)=2(1)4−4(1)3−3(1)−1

2(1)−4(1)−3(1)−1

=2−4−3−1

=−6

Is the remainder same as the value of the polynomial f(x) at zero of (x−1)?

From the above examples we shall now state the fact in the form of the following theorem.

It gives a remainder without actual division of a polynomial by a linear polynomial in one variable.

Given polynomial is f(x)=2x4−4x3−3x−1 and divided by (x−1)

Put x=1 in the given polynomial, we get

f

Answer 2

Given : Dividing the polynomial

2x to tge power of 4 -2 x cube -2x-5 by (

(x-1)

x-1 root of 2x to tge power of 4 +0x cube -2xsquare -2x+5

by diving all these equations we get +5 as answer

See the attachment photo

Hope it helps u

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